The biggest thing in photography is the light. It is possible to bring lighting equipment and set up everything at home, and I do bring lights with me just in case, and use them when I have to. However, I personally prefer to use natural light as much as possible. First of all, because the whole light set up constrains natural flow of things, and the pictures are much more posed compared to natural light pictures.
Therefore, natural light is preferable for candid pictures, and your photography session should take place during daytime to ensure enough light. Big windows are the best, providing very soft flattering light. So if possible, try to arrange a spot in front of the window, with some room for the photographer to stand her back to the window, and you and the baby facing the window.
Background is also important. I am bringing a few choices and stands to set up the background, so it won`t be a problem as long as there is some room for setup.